Simulations and Phenomenology of Topological Defects in Two Higgs Doublet Models

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Abstract

The Two Higgs Doublet Model predicts the emergence of 6 distinct topological defect solutions arising from the breaking of 6 accidental symmetries at the electroweak scale for specific choices of the model parameters. The symmetries permitted in the model can be divided into 3 Higgs Family and 3 general CP symmetries where $ Z_2 $, CP1 and CP2 symmetries predict domain walls; $ \text{U}(1)_\text{PQ} $ and CP3 predict vortices and $ \text{SO}(3)_\text{HF} $ predicts global monopoles. We present numerical kink solutions to the field equations in all three domain wall-forming models along with dynamical simulations of the models in (2+1) and (3+1) dimensions. For each kink solution we define an associated topological current. In all three cases simulations produce a network of domain walls which deviates from power law scaling in Minkowski and FRW simulations. This deviation is attributed to a winding of the electroweak group parameters around the domain walls in the simulations. A local violation of the neutral vacuum condition is observed on the domain walls in our simulations. This violation is attributed to relative electroweak transformations across the domain walls which is a general feature emerging from random initial conditions. For a Two Higgs Doublet Model with exact $Z_2$ symmetry we derive theoretical constraints on model parameters from domain wall domination. We find a value of $\tan\beta > 10^5$ is required for scalar masses of order 100 GeV or greater in/near Standard Model alignment to avoid domain wall domination by present day. We have also performed numerical simulations of the Two Higgs Doublet Model with an approximate $Z_2$ symmetry and an exact $Z_2$ symmetry evolving from biased initial condition. In both cases we find an exponential suppression of the domain wall scaling in these models which can help ameliorate the stringent constraints found in the case of an exact discrete symmetry. For a Two Higgs Doublet Model with softly-broken $Z_2$ symmetry, we relate the size of this exponential suppression to the soft-breaking parameter allowing limits to be placed on this parameter such that domain wall domination can be avoided. Similarly, for the case of an exact $Z_2$ symmetry with biased initial conditions, we relate the exponential suppression to the bias parameter and obtain limits on this parameter to avoid domain wall domination. We present the general equations of motion for perturbations of the electroweak-Higgs sector of the Two Higgs Doublet Models describing the linear-order effects of Two Higgs Doublet Model topological defects coupled to Standard Model particles. These equations are applied to the effects of a domain wall solution on the masses and interactions of electroweak bosons, particularly the photon. A simple calculation using these equations for a scattering interaction of a photon with a background neutral vacuum-violating domain wall suggests that photons of astrophysical energies would experience near-perfect reflection when incident on such a defect. The general version of these equations suggest a much wider scope of applications, for instance, to linear-order interactions of SM particles with cosmic strings and monopoles along with analogous calculations for the fermion sector. We have also investigated the localized effect on the masses of electroweak bosons in the vicinity of $Z_2$ domain walls.

Keyword(s)

Beyond the Standard Model; Cosmology; Discrete Symmetries; Domain Walls; Higgs Physics; Spontaneous Symmetry Breaking

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